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In my third year at university we covered this in an Applied Mathematics course - Calculus of Variations. At the time our lector explained that in the entire fi

In my third year at university we covered this in an Applied Mathematics course - Calculus of Variations. At the time our lector explained that in the entire field of mathematics we've learned over the last 20,000 years or so how to solve about 10,000 different mathematical problems. And of those 10,000 problems, Calculus of Variations comprised about 10. This was one of those 10. I don't know how accurate his numbers are but the point was that this is an extremely narrow field!

Jun8 12y ago
I don't know what 10 problems your professor had in mind but his comment was either in jest or perhaps was made from a narrow mathematical viewpoint: variational principles form the basis of much of Physics, e.g. Hamilton's principle, Fermat's principle, etc. As a side note, for those of you who, like myself, have puzzled how Euler-Lagrange Equations are drived, the answers given to this question are priceless: http://physics.stackexchange.com/questions/885/why-does-calculus-of-variations-work http://physics.stackexchange.com/questions/885/why-does-calc...
cabinpark 12y ago
Unless you misunderstood your professor, what they said is entirely and utterly wrong. Calculus of variations is one of the guiding principles of modern physics. Pull out any textbook on quantum field theory or general relativity and there will be a section dedicated to using calculus of variations to derive the equations of motion. Heck, for a lot of theories, writing down the action and deriving the equations of motion from the Euler-Lagrange equations is the first thing you do. Plus calculus of variations is closely related to differential geometry, which is a massive field. Same with control theory, another massive field with close ties to differential geometry and calculus of variations. I have no idea what point your professor was trying to make.
analog31 12y ago
Long ago, I taught a college math course for a semester. My office mate was teaching differential equations. I asked him if he taught any engineering applications of multivariate differential equations, and he confidently assured me that there were none.
- cabinpark 12y ago
  What are multivariate differential equations? Is that another name for partial differential equations? If so, then I assume your office mate was joking?
  - analog31 12y ago
    Oops, I meant multivariate calculus. But he really was that far out of touch. Not to be too tough on him, he was a grad student teaching assistant with a pure math background.
    - cabinpark 12y ago
      That's a poor reflection on his education then. Even the purest mathematics majors I knew still were aware of the applications of most of what they learnt.

Jun8 12y ago

I don't know what 10 problems your professor had in mind but his comment was either in jest or perhaps was made from a narrow mathematical viewpoint: variational principles form the basis of much of Physics, e.g. Hamilton's principle, Fermat's principle, etc. As a side note, for those of you who, like myself, have puzzled how Euler-Lagrange Equations are drived, the answers given to this question are priceless: http://physics.stackexchange.com/questions/885/why-does-calculus-of-variations-work http://physics.stackexchange.com/questions/885/why-does-calc...

cabinpark 12y ago

Unless you misunderstood your professor, what they said is entirely and utterly wrong. Calculus of variations is one of the guiding principles of modern physics. Pull out any textbook on quantum field theory or general relativity and there will be a section dedicated to using calculus of variations to derive the equations of motion. Heck, for a lot of theories, writing down the action and deriving the equations of motion from the Euler-Lagrange equations is the first thing you do. Plus calculus of variations is closely related to differential geometry, which is a massive field. Same with control theory, another massive field with close ties to differential geometry and calculus of variations. I have no idea what point your professor was trying to make.

analog31 12y ago

Long ago, I taught a college math course for a semester. My office mate was teaching differential equations. I asked him if he taught any engineering applications of multivariate differential equations, and he confidently assured me that there were none.

cabinpark 12y ago
What are multivariate differential equations? Is that another name for partial differential equations? If so, then I assume your office mate was joking?
- analog31 12y ago
  Oops, I meant multivariate calculus. But he really was that far out of touch. Not to be too tough on him, he was a grad student teaching assistant with a pure math background.
  - cabinpark 12y ago
    That's a poor reflection on his education then. Even the purest mathematics majors I knew still were aware of the applications of most of what they learnt.